Abstract In this paper quasi-bimonads on a monoidal category are introduced and investigated. Quasi-bimonads generalize quasi-bialgebras to a non-braided setting. We discuss their representations and investigate the R-matrix of a quasi-bimonad. Such an R-matrix provides a new solution of the version of the Yang-Baxter equation adapted to the situation. We also introduce an equivalent relation on (quasitriangular) quasi-bimonads such that the categories of representations of two (quasitriangular) quasi-bimonads are (braided) monoidal equivalent. Finally, we discuss Drinfeld twists and Hom quasi-bialgebras.

中文翻译：

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准双单体及其表示

摘要 本文介绍并研究了幺半群范畴上的拟双单子。准双单子将准双代数推广到非编织环境。我们讨论它们的表示并研究准双单体的 R 矩阵。这种 R 矩阵提供了适应这种情况的 Yang-Baxter 方程版本的新解。我们还引入了（拟三角）准双单子的等价关系，使得两个（拟三角）准双单子的表示类别是（编织的）幺半群等价的。最后，我们讨论 Drinfeld 曲折和 Hom 拟双代数。